Pore-scale Model Research Articles

Pore scale visualization of thermal-fluid-structural evolution in the ablation of carbon/carbon composites

Understanding the complex thermal and physicochemical mechanisms of an ablated structure is fundamental for the accurate design of highly efficient thermal protection systems. This study proposed a pore-scale comprehensive model combining the lattice Boltzmann and volume fraction methods to couple the heat and mass transfer, flow, carbon interphase and ablation reaction in the ablation of carbon/carbon (C/C) composites. The influences of aerodynamic heat, pressure gradient, and kinematic viscosity on the thermal-fluid-structural evolution in the ablation of C/C composite structure were investigated. The results revealed that the velocity and structure morphology evolution rate in the C/C composite structure increased with an increase in aerodynamic heat. Further, the competitive relationship between the aerodynamic heat and convective heat transfer caused by the structural morphology evolution was identified. Moreover, the velocity and structural morphology evolution rate in the C/C composite structure decreased with an increase in the pressure gradient and kinematic viscosity. The findings of this study can be used as a guide for the design of C/C composite thermal protection systems.

Migration characteristics of oil pollutants into soil pores influenced by surface wettability

ABSTRACT Pore-scale modeling plays an indispensable role in unveiling the migration mechanism of oil pollutants into the water-saturated soil. Navier Stokes equations and conservation of mass, coupled with the phase field method, are employed to investigate the effect of soil wettability on oil pollutants migration into the soil porous media. The results show that the oil-water interface in the migration process does not advance evenly in three wetting states. When the model system is in oil-wetting state, oil pollutants obviously migrate at a higher speed. Through monitoring the evolution of oil front location and analyzing the velocity distribution vertical to the flow direction at the central axis of the model, the channel corresponding to the peak velocity is the dominant flow channel for the oil pollutants. This study will have the potential ability in obtaining the pore-scale migration regulation of oil pollutions as well as more accurately predicting the pollution range.

Pore-scale modeling of oil displacement by pulsating water injection

Pore-scale modeling of oil displacement by pulsating water injection

Combined effects of microstructural characteristics on anisotropic transport properties of gas diffusion layers for PEMFCs

Gas diffusion layer (GDL) plays a key role in proton exchange membrane fuel cells, which provides multi-functions for gas transport, thermal-electrical conduction and mechanical support. Coupling manipulation of different microstructural characteristics could potentially improve transport properties of GDLs. This work proposes an approach to reconstruct heterogenous GDLs and conduct pore-scale modeling to evaluate the anisotropic transport properties. The models are reconstructed using X-ray computed tomography, stochastically reconstruction methods and morphological processing techniques, which consider different fiber diameter, GDL thickness and local porosity distribution type. Combined effects of microstructure characteristics on tortuosity, diffusivity, thermal-electrical conductivity and anisotropic ratios are investigated comprehensively. The results show that the diffusivity with fiber diameter of 7 μm is approximately 7% lower, and the conductivity is 8% higher than that of 9 μm. The anisotropic ratios of diffusivity, thermal conductivity and electrical conductivity range from 1.25 to 1.65, 5 to 20, and 20 to 55, respectively. Local porosity distribution of uniform-fluctuated type, fiber diameter of 7 μm and GDL thickness of 126 μm are suggested to balance diffusivity and thermal-electrical conductivity simultaneously. The methods and results can guide microstructure design of other porous electrodes with higher performance.

Fractal Analysis on the Mapping Relationship of Conductivity Properties in Porous Material

The mapping relationships between the conductivity properties are not only of great importance for understanding the transport phenomenon in porous material, but also benefit the prediction of transport parameters. Therefore, a fractal pore-scale model with capillary bundle is applied to study the fluid flow and heat conduction as well as gas diffusion through saturated porous material, and calculate the conductivity properties including effective permeability, thermal conductivity and diffusion coefficient. The results clearly show that the correlations between the conductivity properties of saturated porous material are prominent and depend on the way the pore structure changes. By comparing with available experimental results and 2D numerical simulation on Sierpinski carpet models, the proposed mapping relationships among transport properties are validated. The present mapping method provides a new window for understanding the transport processes through porous material, and sheds light on oil and gas resources, energy storage, carbon dioxide sequestration and storage as well as fuel cell etc.

Process-based pore-scale simulation of electrokinetic remediation of organic pollutant in porous media

Electrokinetic remediation (EKR) is a promising remediation technology for low-permeability porous media contaminated with organic pollutants. To reveal the processes of nonlinear electroosmotic flow (EOF) and to elucidate the key factors controlling the efficiency of EKR, a process-based pore-scale numerical model was established. Nernst-Planck-Poisson Equation is coupled with Navier-Stokes Equation to describe the transport of species. 1-pK model is applied to evaluate time-varying zeta potential during EKR process. Totally 33 cases are simulated, which include the settings of 3 background concentrations (Cb) of ions in media, 3 pK values, 3 enhanced factor (d, corresponding to reciprocal of diameter of electrode well) values, and two different initial conditions. It is found that all of Cb, pK and d impact EOF and the removal efficiency of organic species. From this study, media with pK of 3.5 and 8.5 are more suitable for EKR with about 5–10 times faster remove rate than media with pK of 5.5. Nonlinear EOF, including decreasing EOF rate and reverse EOF, is more likely to occur in cases with pK of 5.5 and higher values of Cb and d, which can reduce efficiency of EKR by 2–4 times. Using an electrolyte with ion concentration closer to the original background concentrations of ions in soil can favour better removal efficiency.

Pore-Scale Heterogeneities Improve the Degradation of a Self-Inhibiting Substrate: Insights from Reactive Transport Modeling

In situ bioremediation is a common remediation strategy for many groundwater contaminants. It was traditionally believed that (in the absence of mixing-limitations) a better in situ bioremediation is obtained in a more homogeneous medium where the even distribution of both substrate and bacteria facilitates the access of a larger portion of the bacterial community to a higher amount of substrate. Such conclusions were driven with the typical assumption of disregarding substrate inhibitory effects on the metabolic activity of enzymes at high concentration levels. To investigate the influence of pore matrix heterogeneities on substrate inhibition, we use a numerical approach to solve reactive transport processes in the presence of pore-scale heterogeneities. To this end, a rigorous reactive pore network model is developed and used to model the reactive transport of a self-inhibiting substrate under both transient and steady-state conditions through media with various, spatially correlated, pore-size distributions. For the first time, we explore on the basis of a pore-scale model approach the link between pore-size heterogeneities and substrate inhibition. Our results show that for a self-inhibiting substrate, (1) pore-scale heterogeneities can consistently promote degradation rates at toxic levels, (2) the effect reverses when the concentrations fall to levels essential for microbial growth, and (3) an engineered combination of homogeneous and heterogeneous media can increase the overall efficiency of bioremediation.

Study on the material characteristics and barrier mechanism of magnesium potassium phosphate cement/hydroxyapatite cutoff walls for fluoride contamination in phosphogypsum waste stacks

• Magnesium potassium phosphate cement using hydroxyapatite as admixture was prepared as a kind of new cutoff wall material. • The cutoff walls have good adsorption performance for fluorine and could meet the engineering requirements. • Internal structural parameters were analyzed through the pore-scale modeling. • The effect of the cutoff walls for controlling fluorine at 7300 days was simulated by Visual MODFLOW. Large quantities of fluoride were leakaged from the phosphogypsum wastes with rainfall and weathering, which has affected the groundwater environment. As a common engineering material, magnesium potassium phosphate cement (MKPC) with high strength and low permeability was applied in barriers to control the diffusion of contaminants in the groundwater. As an effective fluoride adsorbent, this paper selected hydroxyapatite (HAP) as the admixture for magnesium potassium phosphate cement (MKPC) to prepare the cutoff walls. To explore the feasibility of the cutoff walls applying for fluoride contaminants control, studies were carried out through investigating the appropriate material ratio, adsorption property, migration characteristics, microstructure and engineering performance of MKPC-HAP. Based on the permeability coefficient, compressive strength and adsorption property, the molar mass ratio of magnesium to phosphorus in MKPC and the addition of HAP in the total dry material were determined to be 3:1 and 20 %, respectively. The compressive strength after curing for 7 days was 27.51 MPa and permeability coefficient was 1.904 × 10 −9 m/s. Furthermore, the effective diffusion coefficient and the seepage velocity of fluoride with concentration of 100 mg/L were 7.376 × 10 −8 cm 2 /s and 2.21 × 10 −8 m/s, respectively. The Lattice Boltzmann method (LBM) was applied to simulate the distribution of flow field inside the MKPC-HAP cutoff walls and the connected porosity of MKPC-HAP was 5.12 %. Finally, the service life varied from 12 to 22 years when the fluoride concentration being 50 mg/L with the 1 m cutoff wall thickness. Visual Modflow simulation showed that the migration distance of fluoride was 820 m without the cutoff walls, while it was 402 m after setting the cutoff walls over 7300 days.

Modeling foam propagation in pore network with designated pressure constraints

Foam has been used for decades in petroleum industry for enhanced oil recovery (EOR) due to its mobility adjustment ability. A variety of mechanistic models have been proposed to study foam flow in porous media from multiple scales. In these models, such as population balance models, some important parameters (e.g., foam generation/coalescence rate, flowing foam fraction) are treated empirically since they cannot be obtained from conventional lab experiments. To improve the accuracy and reliability of foam description in these foam-assisted processes, pore network model interwoven with invasion percolation with memory (IPM) method has become a powerful tool in studying foam flow characteristics in porous media, which can predict relative permeability and flowing gas fraction with fully consideration of pore-scale mechanisms of foam generation, destruction, and propagation. However, the assumption of exactly sufficient incremental pressure difference used in conventional IPM-based pore-scale foam modeling is rigorous, not only making it difficult to conduct relevant experimental validations, but also creating potential algorithmic conflicts when simulates displacements in weak foam regime or displacements incorporated with foam coalescence mechanisms. In this study, a novel mixed-sorting rule, which proceeds the displacement by describing the transition between immobile foam bank and mobilized foam flow quantitively, is incorporated into IPM-based foam propagation model. In this way, the immobile foam bank is identified based on effective lamellae generation rate, whereas the mobilized foam flow is distinguished by frontal displacing velocity, respectively. Results estimated with proposed method successfully capture key properties that define pore-scale foam behavior at excessive pressure constraints from formation of immobile foam bank, foam mobilizing pressure thresholds, and fractal dimension of displacement pattern, etc.

Pore-scale modelling of elastic properties in hydrate-bearing sediments using 4-D synchrotron radiation imaging

Gas hydrate contains abundant methane gas, which is considered to be a promising energy resource to mitigate the influence of climate change in the future. Understanding the effect of fluids-solid-hydrate spatial distribution on elastic properties of hydrate-bearing sediments benefits the well-log interpretation. We constructed 4-D hydrate-bearing models covering a wide hydrate saturation range based on high-resolution digital images obtained by Synchrotron Radiation X-Rays Computed Tomography (SRXCT). We analysed the elastic moduli and elastic wave velocities of these models by the static Finite Element Method (FEM). The results demonstrated that the dominant hydrate morphology transits from pore-filling to load-bearing when hydrate saturation increases. At low hydrate saturations, the hydrate formed around some gas bubbles blocks local pore space. Therefore a great enhancement in compressional wave velocity was observed at low hydrate saturations. While the shear wave velocity was less affected due to the presence of thin water films. Based on the simulated results, an empirical model was developed to compute the compressional and shear wave velocities considering the free gas phase. The comparison with some experimental measurements validated the applicability of the model.

Modeling of natural gas self-diffusion in the micro-pores of organic-rich shales coupling sorption and geomechanical effects

A significant amount of the natural gas in shale formations is contained in the micro- and mesopores as dissolved (absorbed) phase and on the surfaces of associated microcracks as (adsorbed) phase. The transport of natural gas in such confined spaces is primarily governed by self-diffusion as could be deduced from Knudsen number. Self-diffusion is governed by the pressure and the space confinement. In this study, realistic kerogen structures possessing both tortuous micropores and larger microcracks were formed and used to assess self-diffusion behavior during the depletion of shale reservoirs through some comprehensive molecular simulation workflow. Analysis of the transport modes revealed transition self-diffusion as the primary transport mechanism in these micropores. The sorption behavior and the mechanical properties were analyzed and incorporated to derive a transition diffusion model that is sensitive to changes in the pore pressure and the stress field. The proposed model was compared and validated against similar work in the literature. The results showed that during a typical production span, a pressure drop influences the sorption profile, the net overburden stress on the pores, and the mean free path, altering the magnitude of self-diffusivity. The calibrated pore scale model produced decent predictive ability with a relative error of 2.5–16%. The implications of structure tortuosity, sorption profile, and pore pressure on the effective diffusion coefficient and gas desorption are discussed in depth. This work provides a novel methodology for studying the effect of coupled multiphysics processes on methane transport in a realistic kerogen geometry, which could be used to calibrate a suitable pore scale model for upscaled reservoir simulation applications and accurate assessment of reservoir dynamics and ultimate recovery.

Numerical studies of spontaneous imbibition in porous media: Model development and pore-scale perspectives

Spontaneous imbibition is a crucial two-phase flow process in a variety of subsurface and industrial applications. Due to the lack of an efficient and reliable pore-scale model, however, how pore-filling events in spontaneous imbibition influence average transport properties (i.e., capillary pressure and relative permeability curves) and entrapment of the nonwetting fluid has not been fully understood. In this work, we first experimentally verify an image-based dynamic pore-network model of spontaneous imbibition that is computationally efficient. Then, case studies of a Nubian sandstone are conducted. We demonstrate that average capillary pressure in cocurrent spontaneous imbibition is significantly overestimated by the widely used Young-Laplace equation. This is because the effects of dynamic pore-filling and air entrapment on average capillary pressure are not parameterized in the equation. Based on our pore-scale numerical results, we elaborate on the competition of pore-filling events under different viscosity ratios of the wetting to the nonwetting fluids. It is found that the filling mode evolves from the co-filling of neighboring pores to the preferential filling of small pores as the nonwetting viscosity increases. Our model will be a useful numerical tool for quantitatively predicting spontaneous imbibition in geological formations. Our findings will help us bridge the gap between pore-scale flow dynamics and the Darcy theory of spontaneous imbibition.

Lattice Boltzmann modelling on pore-scale reactive transport in exothermic reactions of solid blocks for thermochemical energy storage

In this study, a pore-scale numerical model of plate-type reactor is developed to simulate and analyze the coupled CaO/Ca(OH)2 thermochemical heat storage processes based on the lattice Boltzmann method. In the research, the fluid flow, chemical adsorption, mass and heat transfer during hydration reaction are considered. Three different structures with the same porosity of solid particles are designed: in-line, staggered and random patterns. The heterogeneous reaction model with the Langmuir adsorption kinetics is implemented on gas–solid interfaces. The interparticle and intraparticle mass transfer processes are both involved with the help of the lattice Boltzmann method. The distributions of concentration in the gas phase and adsorbed amount in the solid phase are obtained in detail. The conversion rates under three different structures with similar porosity are also compared. Moreover, conjugate heat transfer is applied to simulate the transient temperature distributions in these structures. Heat is released from the solid particles and diffuse to the surrounding area along with the fluid flow. The maximum temperatures of the three structures are 550℃. Besides, the trends of characteristic temperatures over time are also obtained, and the durations above 500℃ are calculated, reflecting the heat storage performances of the different structures. The heat release of three different structures is also compared. It is proved that the structure with staggered blocks is recommended.

Improved kinetics for mineral dissolution reactions in pore-scale reactive transport modeling

Recent numerical investigations revealed that the heterogeneity of the dissolution rate observed in numerous experiments cannot be explained by fluid transport effects. This heterogeneity is attributed to intrinsic surface reactivity. Therefore, reactive transport models (RTM) require parameterization of the surface reactivity for accurate predictions. For this purpose, a nanotopographic parametrization based on surface slope has been recently suggested. In this study, we utilize and improve this parametrization for RTMs of pore-scale systems, from the crystal surface to the single crystal geometry, going beyond the previous reactivity parametrization. 2D and 3D RTMs were developed using COMSOL Multiphysics for calcite systems based on experimental measurements. We compared the results between classically parameterized RTMs, RTMs with new slope parameterization, and experimental data. The effect of flow on dissolution under conditions far-from-equilibrium is found to be negligible, highlighting the importance of surface reactivity in the dissolution reaction. For the first time, the new slope factor was able to accurately reproduce the experimental results on a crystal surface with large field-of-view, large height variability of the topography, and over a long-term reaction period. The new parameterization had greatly improved sensitivity for intermediate reactivity ranges compared to the previous parameterization. A 3D model is used to present the general applicability of the parameterization for use in realistic geometric data sets. Thus, we also show that neglecting surface reactivity in an RTM leads to incorrect predictions regarding the porosity, pore geometry, and surface topography of the system. Our new slope factor can successfully serve as a first-order proxy for the distribution of surface reactivity in 3D pore-scale rock systems. The description of surface reactivity is crucial for accurate long-term modeling of natural rock systems.

Two-phase Flow Dynamics at the Interface Between GDL and Gas Distributor Channel Using a Pore-Network Model

For improved operating conditions of a polymer electrolyte membrane (PEM) fuel cell, a sophisticated water management is crucial. Therefore, it is necessary to understand the transport mechanisms of water throughout the cell constituents especially on the cathode side, where the excess water has to be removed. Pore-scale modeling of diffusion layers and gas distributor has been established as a favorable technique to investigate the ongoing processes. Investigating the interface between the cathode layers, a particular challenge is the combination and interaction of the multi-phase flow in the porous material of the gas diffusion layer (GDL) with the free flow in the gas distributor channels. The formation, growth and detachment of water droplets on the hydrophobic, porous surface of the GDL have a major influence on the mass, momentum and energy exchange between the layers. A dynamic pore-network model is used to describe the flow through the porous GDL on the pore-scale. To capture the droplet occurrence and its influence on the flow, this dynamic two-phase pore-network model is extended to capture droplet formation and growth at the surface of the GDL as well as droplet detachment due to the gas flow in the gas distributor channels. In this article, the developed model is applied to single- and multi-tube systems to investigate the general drop behavior. These rather simple test-cases are compared to experimental and numerical data available in the literature. Finally, the model is applied to a GDL unit cell to analyze the interaction between two-phase flow through the GDL and drop formation at the interface between GDL and gas distributor channel.

Determination of dynamic capillary effect on two-phase flow in porous media: A perspective from various methods

The relationship between capillary pressure and saturation plays a critical role in the characterization of two-phase flow and transport in aquifers and oil reservoirs. This relationship is usually determined under the static condition, where capillary pressure is the only function of saturation. However, considerable experiments have suggested that the dependence of capillary pressure on desaturation rate is under the dynamic condition. Thus, a more general description of capillary pressure that includes dynamic capillary effect has been approved widely. A comprehensive understanding of the dynamic capillary effect is needed for the investigation of the two-phase flow in porous media by various methods. In general, dynamic capillary effect in porous media can be studied through the laboratory experiment, pore- to macro-scale modeling, and artificial neural network. Here, main principle and research procedures of each method are reviewed in detail. Then, research progress, disadvantages and advantages are discussed, respectively. In addition, upscaling study from pore- to macro-scale are introduced, which explains the difference between laboratory experiment and pore-scale modeling. At last, several future perspectives and recommendations for optimal solution of dynamic capillary effect are presented.

Pore-Scale Modeling of Mass Transport in Partially Saturated Cathode Gas Diffusion Layers of Proton Exchange Membrane Fuel Cell

Proton exchange membrane fuel cells (PEMFCs) have the advantages of high specific power, good stability, and zero emissions, making them clean and efficient energy conversion devices. Water management is one of the technical challenges limiting the development of PEMFC, with liquid water blocking the pores and increasing the resistance to mass transport. In this paper, a two-dimensional (2D) multiphase lattice Boltzmann (LB) model is developed to obtain the liquid water morphology within the gas diffusion layer (GDL). A 2D multicomponent flow Lattice Boltzmann model considering electrochemical reactions is established to investigate the effects of water saturation, activation overpotential, and pressure difference between the inlet and outlet gas channels on mass transport. At high water saturation, the liquid water forms water films within the GDL preventing reactive gas transport and water vapor are blocked near the catalyst layer making it difficult to remove. The PEMFC can achieve higher current densities at high activation overpotentials, but oxygen starvation will be exacerbated. Increasing the pressure difference between the inlet and outlet gas passages effectively increases the oxygen concentration and reduces the water vapor concentration in the GDL. The present study improves the understanding of the effect of GDL microstructure on mass transport and performance of PEMFC from the mesoscopic scale.

A multiscale study on the effect of compression on lithium-ion battery separators

Separators play a vital role within Li-ion batteries. Separators allow rapid Li-ion transport while isolating the cathode and anode to prevent electrical short circuits. Herein, the effects of compression on the mechanical and transport properties of the separator were investigated using a multiscale approach. The microscale domain of the separator was stochastically reconstructed based on the scanning electron microscopy images of a Celgard 2400 membrane. The reconstructed model was then imported to perform explicit dynamic simulations to investigate the mechanical behavior of the separator at different compression ratios. A pore-scale model was employed to calculate the effective transport properties of the deformed models. This was then used in a 3D macroscopic multiphysics model to evaluate the impact of compression on the battery performance. The simulation results revealed the effect of compression on the separator's mechanical properties and battery performance from the microscale to macroscale level. The compression of the separator was found to adversely influence the charging performance of the Li-ion battery. When the compression ratio reaches 40 %, the charging performance of the battery decreased significantly. The present study demonstrates a multiscale approach for investigating the effect of compression on Li-ion battery separators. This is a powerful method for optimizing separators in the future.

Pore-scale study of effects of relative humidity on reactive transport processes in catalyst layers in PEMFC

High surface area carbon (HSC) particles can be adopted to increase the specific surface area of catalyst layer (CL) in proton exchange membrane fuel cells. Relative humidity (RH) has a significant effect on the Pt activity inside HSC particles, and the underlying mechanisms need to be further investigated. In this study, a pore-scale model considering the effects of RH on the reactive transport processes inside the CLs is developed. Two kinds of liquid water distributions affected by the RH, including capillary condensation in pores and ultra-thin liquid film on Pt surface, are considered. The liquid water distribution, Pt activity and local oxygen transport resistance (Rlocal) under different RH are studied in detail. It is found that as RH increases from 0.3 to 1.0, the condensed water in micropores of HSC particles increases, resulting in an increase in reactive surface area by about 43 %. Combined effect of the RH, Pt loading, I/C ratio and different kinds of carbon particles is investigated. It is found that due to the lack of sufficient reaction sites, compared with that under a high Pt loading, Rlocal under a low Pt loading is more sensitive to the RH. Besides, since the Pt activity inside HSC particles depends on the condensed water, the Rlocal of HSC particles is more sensitive to the RH than solid carbon particles. Finally, the Rlocal at low ionomer content is more sensitive to RH due to low ionomer coverage on Pt particles. The present study provides a pore-scale model for investigating the coupled effects of RH and CL porous structures on local transport processes, and can facilitate the optimization of CL nanoscale structures for better cell performance.

Pore-Scale Modeling of Immiscible Displacement In Porous Media: The Effects of Dual Wettability

Summary Many naturally occurring porous media contain different types of grains with different wettabilities, therefore, understanding the effect of wettability heterogeneity on multiphase flow in porous media is important. We investigate the immiscible displacement during imbibition in a dual-wettability porous medium by direct pore-scale modeling. We propose a heterogeneous index (HI) to quantify the wettability heterogeneity. Our simulations on the capillary rise in dual-wettability tubes are compared with theoretical predictions, which verifies the numerical method. Our simulation results on the displacement in the dual-wettability porous media show that the wettability heterogeneity has a great impact on the fluid distribution, the capillary pressure curve, and the relative permeability curve. With the increase of wettability heterogeneity (HI), more capillary fingers are found during the displacement, the recovery rate of nonwetting fluid decreases, and the capillary pressure and the relative permeability of the wetting fluid decrease.